**Extraneous and missing solutions - Wikipedia**
https://en.wikipedia.org/wiki/Extraneous_and_missing_solutions

In mathematics, an extraneous solution (or spurious solution) is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem. A missing solution is a solution that is a valid solution to the problem, but disappeared during the process of solving the problem. Both are frequently the consequence of performing operations ...

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